Year: 2026
Type: article
Abstract: In this paper, we study surfaces $$z=\varphi (x,y)$$ z = φ ( x , y ) in Euclidean space that satisfy the equation $$\varphi _{xx}+\varphi _{yy}=\frac{\Lambda }{2}$$ φ xx + φ yy = Λ 2 where $$\Lambda \in \mathbb {R}$$ Λ ∈ R is a real constant. We classify these surfaces when they are the zero level sets of an implicit equation of the type $$f(x)+g(y)+h(z)=0$$ f ( x ) + g ( y ) + h ( z ) = 0 , where f , g and h are smooth functions of one variable. If $$\Lambda =0$$ Λ = 0 , we find a large family of surfaces with interesting symmetry properties. However, if $$\Lambda \not =0$$ Λ ≠ 0 , we show that the surfaces must be either surfaces of revolution or of the type $$z=f(x)+g(y)$$ z = f ( x ) + g ( y ) ; furthermore, explicit parametrizations of these surfaces are obtained.
Source: manuscripta mathematica
Author: Rafael López
Institution: Universidad de Granada
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7140037307